Color Sequences
Every episode of Eleven-Up has a card whose colors are different from one episode to the next. Sequence Basics Each color is composed of three components: red, green, and blue. Each component has up to 9 levels of intensity. This is very similar to the 9-bit RGB colors on the Sega Genesis, except there is one extra level. In the system used by the show, 0 is no intensity, and 8 is full intensity. For example, the color orange could be represented as: Red=8, Green=4, Blue=0. The shorthand for this color is 840. It corresponds to the RGB triplet (255, 128, 0), or hex code #FF8000. "Thumping Ratio" For a given sequence, there is a measure of randomness called the "thumping ratio" (or "TR" for short). Where does this term come from? There was a webpage talking about the funny characteristics of music and sound on the Sega Genesis (see here), and one of the comments was "Music which sounds like the musicians were just picking out random notes and thumping them together!" To find the thumping ratio, follow these steps: #Put all the colors' component values (ranging from 0 to 8) into a table with 3 columns and 11 rows. #Divide all cells' values by 8, so they range from 0 to 1. This is called "normalizing." #Compute the chi-squared value for the table. The chi-squared statistic is a measure of randomness. In computation, if a row has a sum of 0, just regard the row's cells' deviation from the expected value as 0. Likewise, if a column has a sum of 0, regard all cells' deviation in that column as 0. #Evaluate the chi-squared value on the probability density function at 20 degrees of freedom. A 3*11 table has 2*10 = 20 degrees of freedom. #Evaluate a chi-squared value of 18, also at 20 degrees of freedom; this is where the peak of the curve is. #Divide the value from step 4 by the value from step 5; the result ranges from 0 to 1. #For each component (red, green, and blue), pair each component value with its index in the sequence (ranging from 1 to 11). The first color's component is paired with 1, the second color's component is paired with 2, and so on, up to the eleventh and last color, which is paired with 11. #For each component's data pairing in step 7, take the correlation coefficient (r-value) of the data. Then, take the absolute value of each r-value and subtract from 1. #Add up the squares of the values from step 8, then divide the total by the number of nonzero values; the result ranges from 0 to 1. #Take a root of the value in step 9 according to how many values in step 8 were nonzero. If all three values were nonzero, take the cube root; if two values were nonzero, take the square root. #Multiply the result from step 6 by the result from step 10 (both range from 0 to 1), and take the square root. This is the geometric mean of those values. #Take the result from step 11 (again ranging from 0 to 1), and divide it by 1 minus that same value. This is the thumping ratio for the sequence. Season 1 (1988-1989) *1, 9/12/88: Blue, red, yellow, green, cyan, orange, pink, purple, black, white, light blue *2, 9/13/88: Green, blue, red, yellow, dark blue, dark green, purple, white, light blue, orange, brown *3, 9/14/88: Yellow, red, blue, purple, light blue, green, orange, pink, dark green, brown, gray *4, 9/15/88: Orange, red, aquamarine, yellow, blue, dark blue, pink, purple, gold, gray, white *5, 9/16/88: Purple, yellow, pink, green, white, cyan, blue, lime green, orange, light blue, dark purple *6, 9/19/88: Red, yellow, blue, orange, green, purple, yellow-orange, pink, light blue, brown, fuchsia *7, 9/20/88: Hot pink, blue, purple, green, orange, gray, neon yellow, red, cyan, light green, gray *8, 9/21/88: Blue, yellow, green, purple, red, lime green, cyan, white, orange, olive green, light orange *9, 9/22/88: Orange, green, blue, red, cyan, white, purple, pink, gray, black, lavender *10, 9/23/88: White, pink, purple, blue, lime green, yellow-orange, green, orange, cyan, mahogany, yellow *11, 9/26/88: Purple, green, blue, yellow, maroon, red, light blue, gray, orange, olive green, lavender *12, 9/27/88: Red, green, blue, black, white, orange, yellow, purple, pink, light blue, light green *13, 9/28/88: Yellow, yellow-green, green, blue-green, light blue, blue, blue-violet, dark green, white, dark brown, neon orange *14, 9/29/88: Magenta, dark green, light green, dark blue, blue, red, yellow, orange, light gray, dark gray, dark purple *15, 9/30/88: Blue, green, light blue, orange, purple, yellow, dark purple, red, olive green, brown, gray *16, 10/3/88: Yellow, red, blue, purple, black, teal, orange, light blue, green, gray, navy blue *17, 10/4/88: Red, blue, yellow, green, brown, purple, yellow, light brown, light blue, black, orange *18, 10/5/88: Magenta, blue, light blue, green, red, purple, yellow, orange, cyan, blue-violet, black *19, 10/6/88: Light blue, blue, dark gray, yellow, green, purple, black, white, lavender, orange, dark blue *20, 10/7/88: Purple, red, green, light blue, yellow, pink, lime green, blue, black, gray, white *21, 10/10/88: Dark blue, yellow, blue, green, white, red, light blue, light green, gray, gold, cyan *22, 10/11/88: Pink, white, purple, blue, orange, green, fuchsia, light orange, teal, red, yellow *23, 10/12/88: Green, cyan, blue, purple, red, yellow, raw umber, dark gray, light gray, orange, brown *24, 10/13/88: Yellow, yellow-orange, orange, red, blue, white, green, gray, purple, black, dark green *25, 10/14/88: Purple, yellow, light blue, aquamarine, dark blue, orange, blue, red, light purple, dark orange, light brown Season 6 (1993-1994) *1/14/94: Yellow, red, orange, blue-green, gray, tan, brown, maroon, blue, white, green Season 7 (1994-1995) *5/12/95: Maroon, dark maroon, pink, gray, dark gray, violet-blue, yellow, blue, red, orange, light yellow Season 8 (1995-1996) *2/2/96: Red, yellow, orange, pink, bright red, blue, light blue, brown, white, green, dark red *5/6/96: Light gray, red, orange, yellow, green, blue, red-orange, yellow-green, light blue, white, yellow-orange Season 10 (1997-1998) *1/1/98: Red, brown, black, dark green, bright red, dark blue, orange, yellow, blue-green, dark red, dark gray *1/30/98: Blue, green, purple, yellow, orange, red, gray, brown, light blue, hot pink, dark purple Season 15 (2002-2003) *1/1/03: Green, blue, red, yellow, orange, light purple, brown, light blue, purple, white, hot pink *1/3/03: Light blue, orange, light green, purple, yellow, aqua, lavender, white, red, green, blue *4/4/03: Orange, red, green, purple, light blue, blue, lavender, dark purple, flesh-tone, gold, navy blue Season 16 (2003-2004) *9/1/03: Blue, red, yellow, lavender, river blue, deep river, navy blue, purple, hot pink, flesh-tone, dark purple *9/2/03: Dark purple, purple, neon purple, magenta, light blue, red, green, yellow, blue, lavender, orange *9/3/03: Red, black, gray, yellow, dark yellow, blue, blue-green, aqua, orange, dark orange, light gray *9/4/03: Deep river, red, orange, yellow, cyan, green, blue, light purple, dark purple, pink, dark red *9/5/03: Yellow, red, green, purple, orange, blue, hot pink, light blue, black, light purple, dark purple Season 17 (2004-2005) *9/6/04: Cyan, green, white, purple, black, orange, red, yellow, light blue, bright purple, dark blue Season 18 (2005-2006) *12/2/05: Flesh-tone, hot magenta, black, coffee, blue, purple, dark blue, red, pink, green, orange *12/5/05: White, pink, brown, hot pink, navy blue, flesh-tone, lavender, blue, purple, black, bright purple